Theresa May leaves 10 Downing Street on 28 February 2018. ‘Mrs May has only aspirations and magical thinking.’ Photograph: Peter Nicholls/Reuters

The draft of an agreement setting out the terms of the UK’s withdrawal from the EU, published by the European commission on Wednesday, has raised the temperature of the Brexit debate. Hot-headed Eurosceptics are treating it as an act of territorial aggression. Provisions covering the need to avoid a hard border in Ireland through near-total regulatory alignment between north and south has been cast as Brussels annexing Ulster.

That fever can be treated with cold facts. First, the document is only a draft. It is an attempt by the EU side to codify as legal text the deal that was done to complete the first phase of Brexit talks last December. The UK government was entitled to propose its own version but hasn’t done so. Ministers might not like the commission’s draft but, with time running out, they cannot deny that something like it is necessary.

Second, the Irish proposals are the EU’s account of a backstop regime in the absence of other solutions. The December deal had north-south harmonisation as the third of three options – the others being a final-status model of UK-EU trade that removes the issue altogether (a much softer Brexit) and technical wizardry to make border checks invisible. The EU view has been that development of options one and two was Theresa May’s job. She hasn’t done that homework, so Brussels has pressed ahead with option three as the default.

Still, the draft agreement’s presumptions of “a common regulatory area” overseen by EU institutions was always going to be provocative to Brexiters. Some provocation was intended. EU patience with Mrs May’s indecision has worn out. In the absence of concrete proposals from the British side to resolve difficult Brexit questions, the Europeans have chosen to force the issue. It is a risky approach given the appetite on the hard right of the Tory party for sabotaging the whole process.

The prime minister on Wednesday promised a “robust” rejection of proposals that she believes would “threaten the constitutional integrity of the UK”. She means the establishment of different post-Brexit regulatory regimes for Northern Ireland and mainland Britain. That is the corollary of her own insistence that Britain must leave the customs union and single market. The external border has to go somewhere so, if not north-south on the island of Ireland, the logical alternative is east-west in the Irish Sea. That is the outcome most feared by the DUP, on whom Mrs May depends for her parliamentary majority.

These problems would go away if Mrs May knew a better way to meet commitments she made under the December agreement. But every available deal featuring invisible borders crosses red lines that the prime minister drew in 2016 and hasn’t had the courage to revisit.

This is the essence of her trouble: the EU’s proposals cannot be amended without counter-proposals and none exist. Mrs May has only aspirations and magical thinking. There is no Brexit model that satisfies the DUP, the Tory right, the cabinet and parliamentary moderates. Choices have to be made: between economic stability and doctrinaire Eurosceptic purity; between a softer Brexit that is available through negotiation and the hard one that looks like kamikaze nationalistic performance.

The rage of many Brexiters expresses the discovery that the balance of power between the UK and a bloc of 27 countries turns out to be nothing like the dynamic they promised. The EU can set the pace and terms of the negotiation. This is one reason why it was the wrong choice to leave. British influence on the rest of Europe and the world was amplified, not constrained, as a member of the club. Relinquishing that power brings costs that the prime minister doesn’t dare admit in public.

The controversy provoked by the draft withdrawal agreement all flows from a single source: an abdication of leadership. The prime minister is due to make a speech on Friday outlining her proposals for the future relationship between the UK and the EU. Perhaps then she will reveal a hitherto invisible streak of courage and imagination. Perhaps she will rewrite her Brexit priorities to serve country ahead of party. None of the evidence suggests she is capable of that.